Solve for $r$, $ \dfrac{r + 7}{5r - 20} = \dfrac{5}{3r - 12} + \dfrac{6}{4r - 16} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5r - 20$ $3r - 12$ and $4r - 16$ The common denominator is $60r - 240$ To get $60r - 240$ in the denominator of the first term, multiply it by $\frac{12}{12}$ $ \dfrac{r + 7}{5r - 20} \times \dfrac{12}{12} = \dfrac{12r + 84}{60r - 240} $ To get $60r - 240$ in the denominator of the second term, multiply it by $\frac{20}{20}$ $ \dfrac{5}{3r - 12} \times \dfrac{20}{20} = \dfrac{100}{60r - 240} $ To get $60r - 240$ in the denominator of the third term, multiply it by $\frac{15}{15}$ $ \dfrac{6}{4r - 16} \times \dfrac{15}{15} = \dfrac{90}{60r - 240} $ This give us: $ \dfrac{12r + 84}{60r - 240} = \dfrac{100}{60r - 240} + \dfrac{90}{60r - 240} $ If we multiply both sides of the equation by $60r - 240$ , we get: $ 12r + 84 = 100 + 90$ $ 12r + 84 = 190$ $ 12r = 106 $ $ r = \dfrac{53}{6}$